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A branch-and-check algorithm for minimizing the sum of the weights of the late jobs on a single machine with release dates

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  • SADYKOV, Ruslan

Abstract

In this paper we consider the scheduling problem of minimizing the sum of the weights of the late jobs on a single machine (1|rj| [sum] wj Uj ). A branch-and-check algorithm is proposed, where a relaxed integer programming formulation is solved by branch-and-bound and infeasible solutions are cut off using unfeasibility cuts. We suggest two ways to generate cuts. First we show how the algorithm by Carlier [7] can be modified to produce tightened "no-good" cuts. We then demonstratehow to create cuts by using constraint propagation. The branch-and check algorithm proposed is implemented in the Mosel modelling and optimization language. Computational experiments show that our algorithm outperforms the exact approach of P©

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  • SADYKOV, Ruslan, 2005. "A branch-and-check algorithm for minimizing the sum of the weights of the late jobs on a single machine with release dates," LIDAM Discussion Papers CORE 2005057, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2005057
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    1. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    2. Baptiste, Philippe & Peridy, Laurent & Pinson, Eric, 2003. "A branch and bound to minimize the number of late jobs on a single machine with release time constraints," European Journal of Operational Research, Elsevier, vol. 144(1), pages 1-11, January.
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